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The Effect of Directed Movement on the Strong Allee Effect
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| Pengarang | : | Chris Cosner |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 81 (No. 2) |
| Halaman | : | |
| Abstrak | : | It is well known that movement strategies in ecology and in economics can make the difference between extinction and persistence. We present a unifying model for the dynamics of ecological populations and street vendors, which are an important part of many informal economies. We analyze this model to study the effects of directed movement of populations subject to strong Allee effect. We begin with the study of the existence of equilibrium solutions subject to homogeneous Dirichlet or no-flux boundary conditions. Next, we study the evolution problem and show that if the directed movement effect is small, the solutions behave like those of the classical reaction-diffusion equation with bistable growth pattern. We present numerical simulations, which show that directed movement can help overcome a strong Allee effect and provide some partial analytical results in this direction. We conclude by making a connection to the ideal free distribution and analyze what happens under competition, finding that an ideal free distribution strategy is a local neighborhood invader. |
An Asymptotic Analysis of Localized Three-Dimensional Spot Patterns for the Gierer--Meinhardt Model: Existence, Linear Stability, and Slow Dynamics
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 81 (No. 2) |
| Halaman | : | |
| Abstrak | : | Localized spot patterns, where one or more solution components concentrate at certain points in the domain, are a common class of localized pattern for reaction-diffusion systems, and they arise in a wide range of modeling scenarios. Although there is a rather well-developed theoretical understanding for this class of localized pattern in one and two space dimensions, a theoretical study of such patterns in a three-dimensional setting is, largely, a new frontier. In an arbitrary bounded three-dimensional domain, the existence, linear stability, and slow dynamics of localized multispot patterns are analyzed for the well-known singularly perturbed Gierer--Meinhardt activator-inhibitor system in the limit of a small activator diffusivity ????2 ?1. Our main focus is to classify the different types of multispot patterns and predict their linear stability properties for different asymptotic ranges of the inhibitor diffusivity ????. For the range ???? =O?(????−1) ?1, although both symmetric and asymmetric quasi-equilibrium spot patterns can be constructed, the asymmetric patterns are shown to be always unstable. On this range of ????, it is shown that symmetric spot patterns can undergo either competition instabilities or a Hopf bifurcation, leading to spot annihilation or temporal spot amplitude oscillations, respectively. For ???? =O?(1), only symmetric spot quasi-equilibria exist and they are linearly stable on O?(1) time intervals. On this range, it is shown that the spot locations evolve slowly on an O?(????−3) time scale toward their equilibrium locations according to an ODE gradient flow, which is determined by a discrete energy involving the reduced-wave Green's function. The central role of the far-field behavior of a certain core problem, which characterizes the profile of a localized spot, for the construction of quasi-equilibria in the ???? =O?(1) and ???? =O?(????−1) regimes, and in establishing some of their linear stability properties, is emphasized. Finally, for the range ???? =O?(????2), it is shown that spot quasi-equilibria can undergo a peanut-splitting instability, which leads to a cascade of spot self-replication events. Predictions of the linear stability theory are all illustrated with full PDE numerical simulations of the Gierer--Meinhardt model. |
Joint State-Parameter Estimation for Tumor Growth Model
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 81 (No. 2) |
| Halaman | : | |
| Abstrak | : | We present a shape-oriented data assimilation strategy suitable for front-tracking tumor growth problems. A general hyperbolic/elliptic tumor growth model is presented as well as the available observations corresponding to the location of the tumor front over time extracted from medical imaging as MRI or CT scans. We provide sufficient conditions allowing one to design a state observer by proving the convergence of the observer model to the target solution for exact parameters. In particular, the similarity measure chosen to compare observations and simulation of tumor contour is presented. A specific joint state-parameter correction with a Luenberger observer correcting the state and a reduced-order Kalman filter correcting the parameters is introduced and studied. We then illustrate and assess our proposed observer method with synthetic problems. Our numerical trials show that state estimation is very effective with the proposed Luenberger observer, but specific strategies are needed to accurately perform parameter estimation in a clinical context. We then propose strategies to deal with the fact that data is very sparse in time and that the initial distribution of the proliferation rate is unknown. The results on synthetic data are very promising, and work is ongoing to apply our strategy on clinical cases. |
Spectroscopic characterization of 3D photonic crystals
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 10) |
| Halaman | : | 835–844 |
| Abstrak | : | We present a series of optical experiments on 3D photonic crystals suitable for advanced physics laboratory courses or senior capstone projects. The crystals are fabricated from a water solution of monodisperse polystyrene microspheres, with diameters of 200, 220, 370, and 430 nm, using the vertical deposition method. The microspheres self-assemble into a face-centered cubic structure, resulting in a pseudo-bandgap along the [111] direction. We study this bandgap through reflection and angle-resolved transmission spectroscopy using a fiber-optic-coupled USB spectrometer. Our experimental results align closely with predictions based on photonic band diagrams and the Bragg–Snell law, demonstrating the scale invariance of Maxwell's equations. These experiments provide an accessible and engaging platform for students to explore the physics of light interaction with periodic structures. |
Polarization spectroscopy of the 5S –5D5/2 two-photon transition in rubidium
| Pengarang | : | H. C. Busch |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 10) |
| Halaman | : | 824–834 |
| Abstrak | : | We describe a one-color, two-photon polarization spectroscopy experiment on the 5S 1/2–5D5/2 transition in rubidium, suitable for implementation in an advanced undergraduate instructional laboratory. The proposed laboratory module synergistically combines polarization spectroscopy with established fluorescence detection at a wavelength different from the excitation wavelength. The curriculum provided in this paper allows students to compare experimental results with predicted theoretical lineshapes and to study the intensity dependence of the two-photon transition. The module also provides a springboard that enables instructors to expand the curriculum to incorporate additional measurements and theoretical analyses. These activities include collecting spectra on additional transitions, measuring the temperature dependence of the spectral amplitudes, or using the dispersive polarization spectra to frequency stabilize a laser without modulation. |
The study of gamma radiation emitted by natural objects in a student laboratory
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 10) |
| Halaman | : | 815–823 |
| Abstrak | : | Laboratory work conducted at the Atomic Physics Workshop of the Physics Department at Novosibirsk State University (NSU) aims to introduce students to the concepts of gamma-ray radioactivity, radiation measurement units, radioactive decay laws, natural gamma radiation sources, and radioactive series. This work is based on using a high-purity germanium (HPGe) detector. During laboratory sessions, students record gamma radiation spectra for background and several natural samples and calibrate the detector energy scale. While processing the experimental data, students identify radioactive series present in the spectra, estimate the radiation dose received during the laboratory work, plot the energy resolution, calculate the electron rest energy, and explain the features of the spectra associated with gamma-ray interaction with a germanium detector. The work is intended for students of natural sciences who have completed an introductory course in quantum mechanics. |
Scattering from the charge radius of a neutral particle
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 10) |
| Halaman | : | 806–814 |
| Abstrak | : | In the physics curriculum, students normally learn about Rutherford scattering from charged particles in classical mechanics, quantum mechanics, and quantum field theory. This paper provides a pedagogical introduction to the problem of scattering from neutral particles, characterizing an effective charge distribution by a charge radius. Using the Born approximation, the quantum mechanical and field theoretic calculations agree to leading order in the long-wavelength limit but disagree with the classical calculation. |
Unblowing bubbles: Understanding the physics of bubble deflation through a straw
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 10) |
| Halaman | : | 797–805 |
| Abstrak | : | A formal description of the deflation process of a soap bubble attached to a cylindrical tube is provided, with emphasis on quantifying viscous and unsteady effects. Differing from prior studies, the proposed theoretical framework maintains its validity across a wide spectrum of parameter values that define the system. The model is validated through experimental results that can be reproduced at home using liquid soap and a straw, emphasizing its educational aspects. |
Listen! it's a phase transition. The sound of a shape memory alloy
| Pengarang | : | Carlo Andrea Rozzi |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 10) |
| Halaman | : | 789–796 |
| Abstrak | : | Shape memory alloys exhibit a solid-to-solid phase transition that involves a temperature-driven rearrangement of their crystal structure and is responsible for their remarkable properties and numerous technological applications. Here, we propose a simple experiment that analyzes the sound emitted by a Ni40Ti50Cu10 bar at different temperatures as it undergoes a transition between its austenite and martensite phases. We show that the phase transition, which occurs slightly above room temperature, can be qualitatively detected by the ear and quantitatively described using a very simple experimental setup and sound analysis tools. Such a sound-based investigation provides an unusual and engaging way to experimentally introduce solid-to-solid phase transitions, that is suitable for undergraduate courses. |
Common principles behind rainbows and boat wakes
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 10) |
| Halaman | : | 781–788 |
| Abstrak | : | Rainbows and boat wakes may seem unrelated, but they share deep mathematical connections through ray folding, caustics, and Airy interference. This paper explores these principles, which are also relevant for explaining phenomena such as shimmering effects on the bottom of pools and twinkling stars. By revisiting Airy's theories on wavefronts and caustics, we demonstrate their applications not only in optics and for water waves but also in quantum wave packets. Using concepts from undergraduate physics, we highlight the universal patterns that unify these diverse phenomena. |